Geometric Invariant Theory

Course information

Code: MAT1312S
Instructor: Marco Gualtieri
Class schedule: F1-4 BA4010
Evaluation: Three assignments

This is an introductory course in Geometric Invariant Theory. GIT is a tool used for constructing quotient spaces in algebraic geometry. The most important such quotients are moduli spaces. We will study the basics of GIT, staying close to examples, and we will also explain the interesting phenomenon of variation of GIT. As GIT is closely related to symplectic reduction we will also introduce this subject.




The main book we will use is Schmitt’s new book GIT and decorated principal bundles. For extra material I will use the GIT book by Fogarty, Kirwan, and Mumford, Dolgachev’s lectures on invariant theory, as well as Richard Thomas’ notes, Michael Thaddeus’ paper on GIT and flips, as well as his paper on stable pairs. For the material on vector bundles, I’ll use Le Potier’s book on moduli spaces.